The only thing in current times that vaguely resembles this are the international banks, however be assured each one has a sovereign nation whose bread they are required to butter.
Amazon. Google. Facebook. You choose it.
Just wait 10-15 years, pal.
Look into what all 3 of those have to do in regards to demands from China. Many things can't even be run by the actual companies inside that country and instead must be farmed out and licensed to in country companies. Just like Blizzard does not really have WoW in China, people say they do, but they just collect a licensing fee or the whole kerfuffle about Overwatch and the HK stuff some of those tweets were not from actual Blizzard.
When a sovereign state wants to fuck you, it can. Now I do not hold with the idea that one should only concentrate on the power of a sovereign state (which is mostly what classical liberals of the hobbs/locke vein do) and at some point the "private" (whatever that means) collection of power essentially does become the sovereign state and history shows a number of cases where this transition has occurred either through force of arms or mercantilist mechanics. Sovereign states are what they are because they are able to control, defend and/or destroy certain tactically important things.
If you think Google can't be replaced by a few different sovereign states in a very quick fashion you are not analyzing things correctly. It would only take a few warrants to take over certain functionality and keep em running. Most likely things would degrade once they did, but keeping google or facebook running as is would be a simple matter. Even more simple for China since they have hooks already in place in any company that is in country and all of the ones you fear are required to farm out to companies the state has hooks into.
This is not meant to minimize their power or impact but merely to show their nature versus that of sovereign states. They may, in fact, have just as much or more power overall, but they are interwoven, can't really stand on their own and have key vulnerabilities
Shadowrun is actually not a stupid setting. They realize this to some degree. All of the corporations in Shadowrun have a military and espionage wing and they are major sections of each corporation. Indeed this whole idea is one of the major corner stones of why there are shadowrunner for the players to portray. This is a smart creation by the original designers. My only contention is that sovereign states would immediately kill or imprison everyone involved with a corporation trying to do such a thing. The designers of Shadowrun would say this didn't happen during the massive chaos and tumult of the emergence of magic and not being an autisitic douchebag I would say "Ok well that has some plausibility then and it makes a cool setting so I'll go with it." The tumult of Shadowrun not only occupied the sovereign states with nuclear level threats like Dragons, but also forced various corporations to develop their own armies just to defend what they had. So it provided a plausible reason for a corporation to rapidly arm and simultaneously explained how the sovereigns were too occupied to kill them all.
Now compare this to the shallow stupidity of The Outer Worlds.
